ZCB bootstrapping

import numpy as np 
import pandas as pd
from scipy.optimize import minimize
import plotly.graph_objects as go
import matplotlib.pyplot as plt

swap_curve = pd.read_excel("market_data_2023 (1).xlsx", sheet_name=1)
swap_curve = swap_curve.iloc[2:].reset_index(drop=True)
swap_curve.columns = ['Maturity', 'Swap rates (in %)']
swap_curve = swap_curve.dropna()
maturities_ex1 = swap_curve['Maturity'].values
swap_rates = swap_curve['Swap rates (in %)'].values

def convert_maturity(maturity):
    """Converte una scadenza in anni."""
    if 'M' in maturity:
        return int(maturity.replace('M', '')) / 12
    elif 'Y' in maturity:
        return int(maturity.replace('Y', ''))
    else:
        raise ValueError(f"Formato di maturità non riconosciuto: {maturity}")

maturities_ex1 = [convert_maturity(m) for m in maturities_ex1]
swap_rates = swap_rates / 100

df = pd.DataFrame({'Maturity': maturities_ex1, 'swap_rates': swap_rates})
df.head(5)

	Maturity	swap_rates
0	0.083333	0.02516
1	0.250000	0.02647
2	0.500000	0.0308
3	0.750000	0.0314
4	1.000000	0.03239

maturity = df['Maturity']
rate = df['swap_rates']

def NelsonSiegelSvensson(time_to_maturity, b0, b1, b2, b3, t1, t2):
    predicted_yield = (
        b0 +
        b1 * (1 - np.exp(-time_to_maturity / t1)) / (time_to_maturity / t1) +
        b2 * ((1 - np.exp(-time_to_maturity / t1)) / (time_to_maturity / t1) - np.exp(-time_to_maturity / t1)) +
        b3 * ((1 - np.exp(-time_to_maturity / t2)) / (time_to_maturity / t2) - np.exp(-time_to_maturity / t2))
    )
    return predicted_yield

# Obejective Function
def NSSMinimize(params, time_to_maturity, observed_yields):
    def NSSGoodFit(params, time_to_maturity, observed_yields):
        b0, b1, b2, b3, t1, t2 = params
        predicted_yields = NelsonSiegelSvensson(time_to_maturity, b0, b1, b2, b3, t1, t2)
        residuals = predicted_yields - observed_yields
        return np.sum(residuals ** 2)
    

    
    constraints = [
        {'type': 'ineq', 'fun': lambda x: x[0]},               # b0 > 0
        {'type': 'ineq', 'fun': lambda x: x[1] + x[2]},       # b1 + b2 > 0
        {'type': 'ineq', 'fun': lambda x: x[4]},               # t1 > 0
        {'type': 'ineq', 'fun': lambda x: x[5]}                # t2 > 0
    ]

    opt_solution = minimize(
        NSSGoodFit,
        params,
        args=(time_to_maturity, observed_yields),
        method="SLSQP",
    )

    return opt_solution.x

initial_params_1 = (0.03, -0.02, 0.01, 0.005, 1.0, 2.0)
initial_params_2 = (0.025, -0.015, 0.008, 0.004, 1.2, 2.5) 
initial_params_3 = (0.035, -0.03, 0.015, 0.006, 0.9, 2.1)
initial_params_4 = (0.1, 1.5, 1, 0.4, 0.9, 2.)

# Compute 
optimal_1 = NSSMinimize(initial_params_1, maturity, rate)
optimal_2 = NSSMinimize(initial_params_2, maturity, rate)
optimal_3 = NSSMinimize(initial_params_3, maturity, rate)
optimal_4 = NSSMinimize(initial_params_4, maturity, rate)

mat = np.linspace(1, 30, 30) 
yields_1 = NelsonSiegelSvensson(mat, *optimal_1)
yields_2 = NelsonSiegelSvensson(mat, *optimal_2)
yields_3 = NelsonSiegelSvensson(mat, *optimal_3)
yields_4 = NelsonSiegelSvensson(mat, *optimal_4)

# Create DataFrames for each set of yields
new_df = pd.DataFrame({'NSSrates1': yields_1}, index=mat)
new_df['NSSrates2'] = yields_2
new_df['NSSrates3'] = yields_3
new_df['NSSrates4'] = yields_4

new_df.head(5)

	NSSrates1	NSSrates2	NSSrates3	NSSrates4
1.0	0.031240	0.030604	0.031250	0.031440
2.0	0.029729	0.029721	0.029496	0.029051
3.0	0.027030	0.027506	0.026765	0.026349
4.0	0.024972	0.025514	0.024789	0.024672
5.0	0.023743	0.024111	0.023655	0.023800

fig_nss = go.Figure()

# LINE
fig_nss.add_trace(go.Scatter(
    x=new_df.index, 
    y=new_df["NSSrates1"], 
    mode='lines',
    name="Model NSS1",
    line=dict(width=1.3, dash = 'dash')
))

# LINE
fig_nss.add_trace(go.Scatter(
    x=new_df.index, 
    y=new_df["NSSrates2"], 
    mode='lines',
    name="Model NSS2",
    line=dict(width=1.3, dash = 'dash')
))

# LINE
fig_nss.add_trace(go.Scatter(
    x=new_df.index, 
    y=new_df["NSSrates3"], 
    mode='lines',
    name="Model NSS3",
    line=dict(width=1.3, dash = 'dash')
))

# LINE
fig_nss.add_trace(go.Scatter(
    x=new_df.index, 
    y=new_df["NSSrates4"], 
    mode='lines',
    name="Model NSS4",
    line=dict(width=1.3, dash = 'dash')
))


#SCATTER
fig_nss.add_trace(go.Scatter(
    x=df.Maturity, 
    y=df["swap_rates"], 
    mode='markers',
    name="Swap Rates",
    marker=dict(size=6 ,color = 'orangered')
))


fig_nss.update_layout(
    title="Model NSS vs Swap Rates",
    xaxis_title="Maturity",
    yaxis_title="Value",
    font=dict(family="Times New Roman", size=10, color="Black"),
    template="plotly_white",
    showlegend=True,
    width=1000,  
    height=500   
)

# Show the figure
fig_nss.show()

Maturity = np.linspace(-3,30,34)
df3 = pd.DataFrame({'Maturity':Maturity})
df3.loc[0] = [0.083333]
df3.loc[1] = [0.25]
df3.loc[2] = [0.5]
df3.loc[3] = [0.75]

swap_rates = [0.02516, 0.02647, 0.0308, 0.0314]  
df3["swap_rates"] = np.nan  
df3.loc[:3, "swap_rates"] = swap_rates  
df3.loc[4:, "swap_rates"] = new_df["NSSrates1"].values
df3

	Maturity	swap_rates
0	0.083333	0.025160
1	0.250000	0.026470
2	0.500000	0.030800
3	0.750000	0.031400
4	1.000000	0.031240
5	2.000000	0.029729
6	3.000000	0.027030
7	4.000000	0.024972
8	5.000000	0.023743
9	6.000000	0.023137
10	7.000000	0.022928
11	8.000000	0.022947
12	9.000000	0.023087
13	10.000000	0.023282
14	11.000000	0.023496
15	12.000000	0.023708
16	13.000000	0.023909
17	14.000000	0.024096
18	15.000000	0.024265
19	16.000000	0.024419
20	17.000000	0.024557
21	18.000000	0.024682
22	19.000000	0.024796
23	20.000000	0.024898
24	21.000000	0.024991
25	22.000000	0.025076
26	23.000000	0.025154
27	24.000000	0.025226
28	25.000000	0.025292
29	26.000000	0.025352
30	27.000000	0.025409
31	28.000000	0.025461
32	29.000000	0.025510
33	30.000000	0.025555

df3["ZCB_price"] = np.nan
df3["Zero_Rate"] = np.nan
notional = 1.0


for i, row in df3.iterrows():
    if row["Maturity"] <= 1.0:
        rate = row["swap_rates"]
        df3.loc[i, "Zero_Rate"] = rate  
        df3.loc[i, "ZCB_price"] = np.exp(-rate * row["Maturity"]) 

        
for i, row in df3.iterrows():
    if row["Maturity"] > 1.0:
        previous_cashflows = [
            (df3.iloc[j]["swap_rates"] * notional / 2 ) * df3.iloc[j]["ZCB_price"]
            for j in range(int(i))  
        ]
        total_cashflows = sum(previous_cashflows)

        maturity = row["Maturity"]
        coupon = row["swap_rates"] * notional / 2 
        principal_discount = notional  

        zcb_price = (notional - total_cashflows) / (coupon + principal_discount)
        zero_rate = -np.log(zcb_price) / maturity
        df3.loc[i, "ZCB_price"] = zcb_price
        df3.loc[i, "Zero_Rate"] = zero_rate

df3

	Maturity	swap_rates	ZCB_price	Zero_Rate
0	0.083333	0.025160	0.997906	0.025160
1	0.250000	0.026470	0.993404	0.026470
2	0.500000	0.030800	0.984718	0.030800
3	0.750000	0.031400	0.976725	0.031400
4	1.000000	0.031240	0.969243	0.031240
5	2.000000	0.029729	0.915058	0.044384
6	3.000000	0.027030	0.902856	0.034064
7	4.000000	0.024972	0.891722	0.028650
8	5.000000	0.023743	0.881260	0.025281
9	6.000000	0.023137	0.871182	0.022984
10	7.000000	0.022928	0.861308	0.021329
11	8.000000	0.022947	0.851538	0.020089
12	9.000000	0.023087	0.841820	0.019132
13	10.000000	0.023282	0.832133	0.018376
14	11.000000	0.023496	0.822471	0.017767
15	12.000000	0.023708	0.812836	0.017269
16	13.000000	0.023909	0.803233	0.016855
17	14.000000	0.024096	0.793671	0.016506
18	15.000000	0.024265	0.784157	0.016210
19	16.000000	0.024419	0.774699	0.015955
20	17.000000	0.024557	0.765302	0.015734
21	18.000000	0.024682	0.755972	0.015542
22	19.000000	0.024796	0.746715	0.015372
23	20.000000	0.024898	0.737533	0.015222
24	21.000000	0.024991	0.728431	0.015089
25	22.000000	0.025076	0.719411	0.014969
26	23.000000	0.025154	0.710475	0.014862
27	24.000000	0.025226	0.701626	0.014765
28	25.000000	0.025292	0.692864	0.014677
29	26.000000	0.025352	0.684191	0.014597
30	27.000000	0.025409	0.675608	0.014524
31	28.000000	0.025461	0.667115	0.014457
32	29.000000	0.025510	0.658713	0.014395
33	30.000000	0.025555	0.650403	0.014339

save = df3.to_csv('ZCB_prices.csv')